What is the Degree of Freedom of a System?

[DarkDrag0nite]

This is not really the homework. It is the university examination problem. The problem here is many teachers/professors answer differently and not much detailed. And we don't know who was the exact professor who create these problems.

Homework Statement

Instuction: Find the number of "Degree of Freedom (dof)" in the system.

First System

Second System
(Please ignore unreadable words, they're Thai language but you can understand by their variables)

Homework Equations

I don't think there is any relevant equation here.

The Attempt at a Solution

For the First System:

Absolutely, 2 Boxes (M1 and M2) can move left and right. So there are 2 dof.
The 2 sphere (m1 and m2) with the rope can move in circular. So there are 2 dof.
I'm not sure if we also consider 2 sphere that they can move left and right or not ?
If we do, so 6 dof. If not, so 4 dof.
What's should I answer ? 6 or 4 dof ?

For the Second System:

There are two pulleys stuck together (m and M) so we consider as one object which can rotate in 1 circular direction. So there is 1 dof.
The box (MB) can move up and down. So there is 1 dof.
Here is problem, some professors said that the box can move in 3 axis which is 3 dof. Is it reasonable ?
I myself think the box should have only 1 dof which corresponds to the system.
Should answer to this system be 2 dof or 4 dof ?

Any help is appreciative. (I will be at school and not be able to reply for 2 days)

 

[DarkDrag0nite]

Anybody please ?

Maybe I didn't give much information about variable.
R = radius of the pulley
k = spring constant (I don't think we really need it)
M, m = mass of the object

 

[Spinnor]

With the systems you showed consider the variables you would need to completely account for both the kinetic and potential energy of the system in question. For a spring you need to know how much it is compressed. For a mass that moves horizontal you need a velocity. For the pendulum you need a velocity for the motion of the pivot point and another coordinate for the angular position. So for the first example you need four position coordinates and four velocities. So eight degrees of freedom for the first example?

If this is not right I hope it is corrected.

 

[DarkDrag0nite]

With the systems you showed consider the variables you would need to completely account for both the kinetic and potential energy of the system in question. For a spring you need to know how much it is compressed. For a mass that moves horizontal you need a velocity. For the pendulum you need a velocity for the motion of the pivot point and another coordinate for the angular position. So for the first example you need four position coordinates and four velocities. So eight degrees of freedom for the first example?

If this is not right I hope it is corrected.

I get the idea. But do we count DOF from the spring too ?

 

[SammyS]

Have you learned any methods for analyzing the number of Degree of Freedom for a system? --- any theorems?

Without more details (such as what motions M_B can have) these appear to have no particular correct answer.

If no other instructions were given, I would be inclined to think that the motions are in the plane of the page.

 

[Spinnor]

I get the idea. But do we count DOF from the spring too ?

I would like to be corrected, but with four position coordinates and four velocities we can completely account for both the kinetic and potential energy for all parts of the first system and that number eight gives you the degrees of freedom?

 

[DarkDrag0nite]

If no other instructions were given, I would be inclined to think that the motions are in the plane of the page.

No other instructions were given in this exam.

Have you learned any methods for analyzing the number of Degree of Freedom for a system? --- any theorems?

I'm currently in high school and never learn such these theorems. I know only DOF is how many axis the object can move/rotate. (Of course, my friends know nothing) Wikipedia and many website do not give enough information. Could you please advise me ?

Thank in advance.

 

[DarkDrag0nite]

I would like to be corrected, but with four position coordinates and four velocities we can completely account for both the kinetic and potential energy for all parts of the first system and that number eight gives you the degrees of freedom?

I've checked. For the first system, there is four choices:
1. 2DOF
2. 3DOF
3. 4DOF
4. 6DOF
For the second system, it is writing test.

Anyway, Please ignore the choices. The choices are usually incorrect.

 

[Spinnor]

I've checked. For the first system, there is four choices:
1. 2DOF
2. 3DOF
3. 4DOF
4. 6DOF
For the second system, it is writing test.

Anyway, Please ignore the choices. The choices are usually incorrect.

I looked in "Lagrangian Dynamics" a Schaums outline for a definition of degrees of freedom and it looks as though I was wrong but on the right track. In what I wrote above you only need to count how many coordinates you need to completely describe the position of the systems parts and not the velocities. So it looks like the answer is 4DOF.

From page 15 of the book:

"degrees of freedom of the system. This is defined as: The number of independent coordinates (not including time) required to specify completely the position of each and every particle or component part of the system."

Now we both know %^)

 

[DarkDrag0nite]

From page 15 of the book:

"degrees of freedom of the system. This is defined as: The number of independent coordinates (not including time) required to specify completely the position of each and every particle or component part of the system."

Now we both know %^)

Thank you so much ! This is exactly what I'm looking for. :)